Abstract: The general topic of the talk has to do with the question of understanding how paths of random walks can create large separating interfaces. This question has in particular been investigated in the context of the analysis of the disconnection time by random walk of a discrete cylinder with a large connected base. We will present an overview of some of the results, and paradigms, which have by now emerged, and explain how the above problem is related to questions of percolation and to the model of random interlacements.